View source for Predicate symbol

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''predicate letter''

A notation for some concrete predicate or relation. E.g., the symbol $\leq$ often denotes the order relation on the real numbers; it is a $2$-place predicate. In the formal structure of a language, the symbols denoting predicates must be used, in a well-defined way, for constructing expressions of the language. In particular, if $P$ is an $n$-place (or $n$-ary) predicate symbol, then the following rule should be among the syntactic rules for forming expressions in the formalized language:  "If $t_1,\ldots,t_n$ are terms, then $P(t_1,\ldots,t_n)$ is a formula". Thus, predicate symbols are syntactically used to form formulas, and semantically denote predicates.

====References====
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<TR><TD valign="top">[1]</TD> <TD valign="top">  S.C. Kleene,   "Introduction to metamathematics" , North-Holland  (1951)</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  Yu.L. Ershov,   E.A. Palyutin,   "Mathematical logic" , Moscow  (1970)  (In Russian)</TD></TR>
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====Comments====
A predicate symbol is also called a ''relation symbol''.

====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  Yu.I. Manin,   "A course in mathematical logic" , Springer  (1977)  (Translated from Russian)</TD></TR>
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